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THE

PREFACE.

I

**N the Year 1711, Mr. Tipper, the Author of, The Ladies Diary, published a Book Monthly, called, Delights for the Ingenious; but for ReaJons by him mentioned in the Diary, 1712. be. then laid 'em afide, much Importunity has been used to have the fame re-affumed and continued; as there. is nothing of this Nature published, but what is in the above-mention'd Diary yearly, (except The Philofophical Tranfactions) and the Limits there, are fo narrow, that but very little can be inferted; and that is oftentimes low and trifling, and fometimes impoffible, Several of the most difficult Questions returned with only the bare Numbers, without any algebraical Process, fo that Beginners in those Studies are little inftructed thereby, as if no fuch Thing had ever been inferted; and we may add, that Solutions abfurd and erroneous are given as true. Witness those of Questions the 172, and 174 1733 as answered in 1734, especially the Prize Question, 1733, answer'd by Mr. C. Mafon, by which he has demonftrated to all the World, bis Ignorance in Trigonometry, and I think at the leaft, it argues want of Care alfo, in the Author, to put in a Solution, fo foreign from the Truth.

The Defign of the enfuing Treatife is to correct all this, wherein the Answers to the Questions shall be all at full Length; and though it be chiefly defigned for the ftudious in Mathematicks, yet it will also comprehend Enigma's, Paradoxes, &c.

The Mathematick Arts need no Recommendation, they carry their own Reward with 'em, by leading us to Truth by the nearest Way, and with the greateft certainty: The Antients held them in fo much esteem, that their Kings were not only Encouragers of them, but Students in them, they accounting that Perfon unfit to govern the World who knew not what the World was: They give us more just and adequate Notions of the Univerfe, and of the Situation of the Parts and extent of our own System; "and do molt powerfully demonftrate to us the Existence and Attributes

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of fome Almighty defigner; to prove this to any Perfon, one need only to bid him confider the Sun with that inSupportable Glory and Lustre that furrounds it: Fu demonftrate the vast Distance, Magnitude, and Heat of it: "To represent to him the Chorus of Planets moving periodically by uniform Laws, in their feveral Orbits about it; aff rding a regular Variety of Aspects; guarded fome of them by jcondary Planets, and as it were emulating "the State of the Sun; and probably all poffeft by proper "Inhabitants, to remind him of thofe furprizing Vifits the "Comets makes us; the large Trains, or uncommon Splen "dor which attends them; the far Country they come from; and the Curiofity and Horror they excite, not only among us, but in the Inhabitants of other Planets, who also may be up to fee the Entry and Progress of thefe Minifters of "Fate: To direct his Eye and Contemplation through. thoje azure Fields, and vaft Regions above him, up to the fixed Stars, that radiant numberless Hot of Heaven; "and to make him understand how unlikely a Thing it is, "that they should be placed there only to adorn and beSpangle a Canopy over our Heads, and much less to supply "the Places of fo many Glow-Worms, by affording a feeble

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Light to our Earth, or even to all our Fellow Planets: "To convince him, that they are fo many other Sus, with "their feveral Regions and Sets of Planets about them : "To fhew him by the Hlp of Glaffes, ftill more and more "of these fix'd lights, and to beget in him an Apprehenfion "of their unaccountable Numbers, and of the immenfe "Spaces, that lye retired beyond our utmost Reach, and " even Imagination: I fay, one need but do this, and explain "to him fuch Things as are now known almost to every "Body, and by it to fhew that if the World be not infinite, "it is infinito Similis; and therefore jure a magnificent "Structure, and the Work of an infinite Architect

Such are the Advantages we receive from the Science of Mathematicks, and as long as the Investigation of Truth continues to be pleafant (which will be always to intelligent and rational Minds) fo long will alfo the above-named Study be: Iball adjoin to this, the excellent Dr. Cotes's Preface to the ad Edition of Sir Ifaac Newton's Principia, as an Introduction to the following Work, in which he shews the Prebeminence of experimental Philofophy above the Hypothetical. February the 26th, *733-4 &c.

Mifcellanee

Mifcellanea Curiofa, &c.

Extracted from Dr. R. COTE S.

T

HOSE who have treated of Natural Philofophy may be nearly reduced to three Claffes. Of thefe, fome have attributed, to the feveral Species of Things, Specific and Occult Qualities;. on which, in a Manner unknown, they make the Operations of the feveral Bodies to depend. The Sum of the Doctrine of the Schools, derived from ARISTOTLE and the Peripatetics, is herein contained. They affirm, That the feveral Effects of Bodies arife from the particular Natures of thofe Bodies: But whence it is that Bodies derive thofe Natures, they don't tell us, ; and therefore they tell us nothing. And being entirely employed in giving Names to Things, and not in fearching into Things themfelves, we may fay they have invented a philofophical Way of Speaking, but not that they have made known to us true Philofophy.

OTHERS therefore, laying afide that useless Heap of Words, thought to employ their Pains to better Purpose. Thefe fuppofed all Matter homogeneous; and that the Variety of Forms, which is feen in Bodies, arifes from fome very plain and fimple Affections of the component Particles: And by going on from fimple Things, to those which are more compounded, they certainly proceed right; if they attribute no other Properties to those pri

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mary Affections of the Particles, than Nature has done. But when they take a Liberty of imagining at Plea fure unknown Figures and Magnitudes, and uncertain Situations and Motions of the Parts; and moreover of fuppofing occult Fluids, freely pervading the Pores of Bodies, endued with an all-performing Subtilty, and agitated with occult Motions, they now run out into Dreams and Chimera's, and neglect the true Conftitution of Things; which certainly is not to be expected from fallacious Conjectures, when we can fcarce reach it by the most certain Obfervations Thofe who fetch from Hypothefes the Foundations on which they build their Speculations, may form indeed an ingenious Romance, but a Komance it will ftill be.

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THERE is left then the third Clafs, which profefs Experimental Philofophy. Thefe indeed derive the Caufes of all Things from the moft fimple Principles poffible; but then they affume nothing as a Principle, that is not proved by Phenomena. They frame no Hypothefes, nor receive them into Pailofophy, otherwife than as Questions whofe Truth may be difputed. They proceed therefore in a two-fold Method, Syntherical and Analytical. From fome felect Phe omena they deduce by Analysis the Forces of Nature, and the more fimple Laws of Forces; and from thence by Synthefis hew the Conftitution of the rest. This is that incomparably best Way of Philofophizing, which Sir Ifaac Newton moft justly embraced before the reft; and thought alone worthy to be cultivated and adorn'd by his excellent Labours. Of this he has given us a most illuftrious Example by the Explication of the Syftem of the World, moft happily deduced from the Theory of Gravity. That the Virtue of Gravity was found in all Bodies, others fufpected, or imagined before him; but he was the only and the firt Philofopher that could demonftrate it from Appearances, and make it a Solid Foundation to the most noble Speculations.

1kNow indeed, that fome Perfons, and thofe of great Name, prepoffefs'd with certain Prejudices, are unwilling to affent to this new Principle, and are ready to prefer uncertain Notions to certain. It is not my Intention to detract from the Reputation of thefe eminent Men: I fhall only lay before the Reader fuch Confiderations as

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will enable him to pafs an equitable Sentence in this Difpute.

THEREFORE that we may begin our reafoning from what is moft fimple and nearest to us: Let us confider a little what is the Nature of Gravity with us on Earth, that we may proceed the more fafely when we come to confider it in the Heavenly Bodies, that lie at fo vast a riftance from us. It is now agreed by all Philofophers, that all circumterreftrial Bodies gravitate towards the Earth; that no Bodies really light, are to be found, is now confirmed by manifold Experience. That which is Relative I evity, is not true I evity, but apparent only; and arifes from the preponderating Gravity of the contiguous Bodies.

MOREOVER, as all Bodies gravitate towards the Farth, fo does the Earth again towards Fodies. That the A&tion of Gravity is mutual, and equal on both Sides, is thus proved. Let the Mafs of the Earth be diftinguifhed into any two Parts whatever either equal, or any how unequal: Now if the Weights of the Parts towards each other, were not mutually equal, the leffer Weight would give Way to the greater and the two Parts joined together, would move on ad infinitum in a right Line, towards that Part to which the greater Weight tends; altogether again ft Experience. Therefore we muft fay, that the Weights of the Parts are conftituted in équinbrio; that is, that the Action of Gravity is mutual and equal on both Sides.

THE Weights of Bodies at equal Diftances from the Centre of the Earth, are as the Quantities of Matter in the Bodies. This is collected, from the equal Acceleration of allodies, that fall from a State of Reft, by the Force of their Weights; for the Forces, by which unequal Bodies, are equally accelerated, must be proportional to the Quantities of the Matter to be moved. Now that all Bodies are in falling equally accelerated appears from hence; that when the Refiftance of the Air is taken away, as it is under an exhaufted Receiver, Eodies falling defcribe equal Spaces, in equal Times; and this is yet more accurately proved by the Experiments of Pendulums.

THE attractive Forces of Bodies at equal Diftarces, are as the Quantity of Matter in the Eodies, or firce

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Bodies

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